To find the distance between the two points \((-2, -1)\) and \((2, 4)\), we can use the distance formula derived from the Pythagorean Theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, the coordinates are:
- \( (x_1, y_1) = (-2, -1) \)
- \( (x_2, y_2) = (2, 4) \)
Now, substitute the values into the formula:
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Calculate \(x_2 - x_1\): \[ x_2 - x_1 = 2 - (-2) = 2 + 2 = 4 \]
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Calculate \(y_2 - y_1\): \[ y_2 - y_1 = 4 - (-1) = 4 + 1 = 5 \]
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Now substitute these results into the distance formula: \[ d = \sqrt{(4)^2 + (5)^2} = \sqrt{16 + 25} = \sqrt{41} \]
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Now, we can calculate \(\sqrt{41}\). The approximate value of \(\sqrt{41}\) (using a calculator) is about \(6.403\).
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Finally, rounding to the nearest hundredth gives \(6.40\).
Thus, the correct answer is A. 6:40 (written here as 6.40).
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